Digital compensator

ABSTRACT

An approach to digital compensation uses a particular structure for a digital pre-distorter (DPD) which acts as a relatively accurate pre-inverse of a non-linear circuit (e.g., a non-linear transmit chain involving digital-to-analog converter (DAC), lowpass filter, modulator, bandpass filter, and power amplifier) while making use of a relatively small number of parameters that characterize the non-linearity and/or parameters that provide accurate linearization without requiring continual updating.

BACKGROUND

This invention relates to digital compensation of a non-linear circuit,and in particular, to linearization of a non-linear power amplifier andtransmitter chain.

A concept of applying a digital compensation to restore the quality ofan original signal passed through a circuit is a routine. A poweramplifier in a radio of a wireless base station or handset iscompensated digitally in the baseband to minimize the spectral leakageinto adjacent channels. An audio amplifier in a speaker is compensateddigitally to achieve high fidelity. In many such examples, variants ofVolterra series have been adopted to account for dynamical nature ofnonlinearity. Wiener, Wiener-Hammerstein, General Memoryless Polynomialare popular structures for digital pre-distorters, which are used tomodify an input signal prior to passing through a non-linear circuit. Ingeneral, these structures have an exponential complexity if thepolynomial order exceeds 3 to 5, as well as robustness issues due tosensitivity of compensator parameters to variations of a particulardevice (Device Under Test, DUT), including process, temperature, supplyvoltage, and other operating conditions.

Referring to FIG. 1, in an example of a linearization of a radio poweramplifier, a digital input signal x[n] at a baseband or intermediatefrequency is passed through a Digital Pre-Distorter (DPD) 110 to producea “pre-distorted” input y[n], which is passed through a transmit chain140 to produce a driving signal p(t) that drives an antenna 150. Thetransmit chain may include a Digital-to-Analog Converter (DAC) 142, ananalog lowpass filter (LPF) 144, and a modulator (e.g., multiplicationby a local oscillator) of the output of the LPF 144. The output of themodulator is passed to a power amplifier (PA) 148. The PA 148, as wellas other elements in the transmit chain, may introduce non-linearities,which may be manifested in the driving signal p(t) as harmonic and/orintermodulation distortion of the input signal x[n]. To overcome thesenolinearities, the DPD 110 also introduces non-linearities that areintended to “pre-invert” (i.e. pre-distort) the non-linear effects ofthe transmit chain. In some examples, the DPD performs thetransformation of the desired signal x[n] to the input y[n] of thetransmit chain by using delay elements 120 to form a set of delayedversions of the desired signal, and then using a non-linear polynomialfunction 130 of those delayed inputs. In some examples, the non-linearfunction is a Volterra series:y[n]=h ₀+Σ_(p)Σ_(τ) ₁ _(, . . . ,τ) _(p) h _(p)(τ₁, . . .τ_(p))Π_(j=1 . . . p) x[n−τ _(j)]In some examples, the non-linear function is reduced set of Volterraterms, for example a delay polynomial:y[n]=h ₀+Σ_(p)Σ_(τ) h _(p)(τ)x[n−τ]|x[n−τ| ^((p-1))

In order to invert the non-linear effects of the transmit chain, ingeneral, a relatively large number of terms of such a seriesrepresentation are needed, and the coefficients of those terms (e.g.,the h_(p) terms) must be accurately set. In general, the coefficients insuch approaches are continually updated to maintain good linearization.Various approaches to such continual updating are used, for example,based on incremental updates using y[n] and observation of p(t) (e.g.,after demodulation).

SUMMARY

In a general aspect, an approach to digital compensation uses aparticular structure for a digital pre-distorter (DPD) which acts as arelatively accurate pre-inverse of a non-linear circuit (e.g., anon-linear transmit chain involving digital-to-analog converter (DAC),lowpass filter, modulator, bandpass filter, and power amplifier) whilemaking use of a relatively small number of parameters that characterizethe non-linearity and/or parameters that provide accurate linearizationwithout requiring continual updating.

In general, this approach is more closely related to the underlyingsources of non-linearity arising from the modulation and subsequent(e.g., non-linear) amplification of the modulated signal. In particular,the approach more directly captures harmonic and intermodulationdistortion effects without requiring a large number of parameters.

In one aspect, in general, a pre-distorter implements an overallnon-linear transformation of a sampled input signal u[n] (e.g., anupsampled version of a baseband encoding of a desired signal to betransmitted) to yield an input y[m] to a transmit chain. The overallnon-linear transformation is implemented using a combination of timefiltered versions of linear and non-linear functions of the inputsignal. In this description, these time filtered versions are referredto as basis functions of the input signal. Some examples of such basisfunctions includew _(i) =G _(i)(ƒ_(i)(u))where ƒ_(i) (u) may be a non-linear function of u, for example, |u|^(k),and G_(i)( ) may be a linear time domain filtering.

In some examples, a set of basis functions is combined using a “balancedpolynomial” form, which can be expressed as:

${y\lbrack n\rbrack} = {\sum\limits_{k}{a_{k}\left( {\left( {\prod\limits_{i}\left( {w_{i}\lbrack n\rbrack} \right)^{b_{k,i}}} \right)\left( {\prod\limits_{j}\left( {w_{i}^{*}\lbrack n\rbrack} \right)^{c_{k,j}}} \right)} \right)}}$where ${{\sum\limits_{i}b_{k,i}} = {1 + {\sum\limits_{j}c_{k,j}}}},$

In some cases, the exponents {b_(k,i)} and {c_(k,j)} are predetermined,and the parameters Θ={a_(k)} are determined, for example, using variousapproaches to system identification.

In some examples, the parameters for a device are determined prior tooperation, for example, at a fabrication, manufacture, deployment,and/or periodic maintenance time, and then set for subsequent operation.In some examples, different sets of parameters are determined fordifferent operating conditions (e.g., operating temperature, supplyvoltage, etc.), and in operation different sets of parameters are usedaccording to sensing of the operating conditions. In some examples,external parameters such as temperature, supply voltage, output power,modulation mode, part age, sampling rate and part signature are inputsto a previously configured predictor unit. Based on these, the unitdetermines the regime of operation and outputs updated coefficients forthe compensator. In some examples, the part signature is obtained byshort fabrication-time characterization (e.g. few tones or a specialtransmit sequence).

One or more approaches described above have advantages including reducedoperation-time computation complexity, thereby reducing powerrequirements and use of other computation-related resources, whileproviding relatively accurate linearization (e.g., relative to otherapproaches that use comparable computation resources). By using astructure of the pre-distorter that matches the non-linear structure ofthe circuit, the number of coefficients needed to accurately linearizethe system is reduced and these parameters are more robust to variationof the system, thereby avoiding the need to continually update theparameters based on the observation of the output signals (e.g. p(t)).Note that the predictor can continuously update the coefficients inresponse to, for example, temperature changes, or supply voltagechanges.

Other features and advantages of the invention are apparent from thefollowing description, and from the claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of a conventional digital pre-distortionapproach;

FIG. 2 is a block diagram representing a number of embodiments of thepresent approach;

FIG. 3 is a block diagram illustrates a coefficient interpolationapproach;

FIG. 4 is a block diagram that shows a operation-time parameterestimation approach;

FIG. 5 is a block diagram that shows a pre-operation coefficientmodeling approach;

FIG. 6 is a block diagram showing a combined coefficient interpolationand operation time parameter estimation approach;

FIG. 7 is a block diagram of an exemplary basis formation and polynomialcombination embodiment; and

FIG. 8 is a block diagram of an alternative basis formation approachincorporating normalization.

DESCRIPTION

Referring to FIG. 2, a first embodiment of a Digital Pre-Distorter 200accepts a desired input signal x[m] in digital form (e.g., 12-14 bitsper time sample), sampled at a sampling rate sufficient to represent thebandwidth (e.g., 20-120 MHz) of the desired signal. In general, theinput signal is complex, with the real and imaginary parts representingquadrature components of the signal to be transmitted. For example, thedesired input is a baseband encoding (e.g., an OFDM encoding) of one ormore channels of communication, for instance, for a cellular telephonetransmitter (e.g., according to an LTE communication standard). Theinput signal is upsampled using a conventional upsampling/interpolationcomponent 210, for example, in some embodiments by a factor equal to oneplus the degree of nonlinearity of interest in the transmit chaindivided by two (e.g., if nonlinearity of interest is 7^(th) order, thenupsampling by a factor of four is used), and then optionally filtered.Upsampling enables the DPD by shrinking the spectrum to avoid aliasingof undesirable harmonics in the target band.

In some examples, an optional LTI (Linear Time Invariant) filteringcomponent 212 processes the signal after upsampling. The LTI filter isselected to “mimic” the long-term behavior of the elements of thetransmit chain 140, for example, for the DAC 142, the LPF 144, etc. Forexample the fixed-coefficient reconstruction filter mimics thezero-order hold properties of the DAC. The upsampled and filtered inputsignal u(n) is then used to compute S basic signals, w₁[n] through w_(S)[n], each sampled at the upsampled rate, using a set of basis formationelements 220 a-s, most of which represent non-linear transformations(e.g., polynomial function) of the input. The basis formation canincorporate polynomial function of the input, or alternativelynon-polynomial function, for example, a polynomial X|X|², or anon-polynomial (X|X|²)/avg(|X|²). The basis signals are applied tobalanced polynomial computation element 230, or in alternativeembodiments another form of non-linear combination, which outputs acombined signal z[n] at the upsampled rate. This combined signal is thendownsampled in a downsampling/filtering component 240, and optionallyfurther filtered in a LTI filtering component 242, for example, yieldingthe original sampling rate of the input signal x[m], to produce anoutput y[m] of the DPD 200.

Referring to FIG. 3, in some embodiments, the output y[m] of the DPD 200is passed through a transmit chain 140 to produce the driving signalp(t) for the antenna 150 of the transmitter. As shown in FIG. 2, the DPD200, and more particularly the balanced polynomial computation isconfigured according to numerical parameters, the DPD coefficients Θ235. In this embodiment, these coefficients are determined using adatabase of coefficients 344, and values that essentially characterizethe operation “regime” (i.e., a class of physical conditions) of thetransmit chain. These values (e.g., quantitative or categorical digitalvariables) include environment variables 342 (e.g., temperature,transmitter power level, supply voltage, frequency band) and/or a part“signature” 343, which represents substantially invariantcharacteristics and which may be unique to the electronic parts of thetransmit chain 140. The coefficient interpolator 340 takes these inputsand the coefficient database and outputs corresponding DPD coefficients235. A variety of approaches may be implemented by the coefficientinterpolator, including selection and/or interpolation of coefficientvalues in the database according to the inputs, and/or applying amathematical mapping of the input represented by values in thecoefficient database.

Referring to FIG. 4, in another embodiment, the DPD coefficients 235 aredetermined during operation of the system by using a receive chain 430processes a sensing of the output p(t), and though substantially lineardemodulation, and digitization, produces a digital output q[m] at thesame sampling interval as the input y[m] of the transmit chain. In someexamples, the coefficients are adjusted in a substantially continuousmanner during operation, while in other examples, the coefficients areupdated relatively infrequently in batches (e.g., once an hour, day,etc.) using non-operational inputs. The determination of theseparameters is discussed more fully below, and generally relies onsensing of an output of the transmit chain 140, and processing thatsensed output using a receive chain 330, which is assumed to besubstantially linear.

Referring to FIG. 5, an approach to forming the coefficient database 344(see FIG. 3) makes use of an analysis the transmit chain 140 prior tooperational use. More generally, a set of instances of transmit chains(e.g., using separately manufactured parts) are analyzed to samplemanufacturing and other part-to-part variations. Generally, differenttest signals x[m] are used to drive the transmit chain 140, andcorresponding input y[m] and received output q[m] (i.e., afterdemodulating through the received chain 430), are used to estimate DPDcoefficients 235 under various environmental conditions. The DPDcoefficients 235 and corresponding environment variables 342 areprovided to the coefficient modeler 560, which stores them (optionallypre-processing them, for example, for from a piecewise linear model) inthe coefficient database 344.

Continuing to refer to FIG. 5, each instance of the transmit chain maybe characterized by passing specific test signals through the transmitchain 140 and using a signature measurement module 550 to determinesignature values (e.g., quantitative or categorical values) from thosemeasurements. For example, multi-tone test signals may be passed throughthe transmit chain and the magnitude of distortion products may bemeasured and recorded as elements of the part signature. As part of themanufacturing or other pre-operational stage, the part signature for atransmit chain is provided in association with that transmit chain, andused in operation, for example, as part signature 343 as illustrated inFIG. 3. For example, the part signature may be stored on a computerreadable medium (e.g., non-volatile semiconductor memory) in, coupledto, or otherwise associated with the transmit chain or its components.When used by the DPD 200, the part signature imparts specificfunctionality on the DPD to compensate for non-linearities of thespecific instance of the transmit chain.

It should be understood that environment variables and signaturevariables may be used independently or in combination. Also, it shouldbe understood that the coefficient interpolator 340 (e.g., FIG. 3) mayimplement various forms or interpolation or approximation as long asthey are compatible with the coefficient modeler 560 (e.g., FIG. 5).Such techniques can include the use of a piecewise linear interpolationas a non-essential example. Other ways of mapping from the environmentand signature variables include use of other piecewise smooth functions,kernel approach, etc. . . . .

Referring to FIG. 6, yet another embodiment combines aspects shown inFIG. 3 and in FIG. 4, namely that the DPD coefficients 235 depend notonly on an interpolation based on a coefficient database 344 andenvironment variables 342 and/or part signature 343, but also depend onfeedback of sensed and demodulated via a receive chain 330 of the outputof the transmit chain 140.

Referring to FIG. 7, and also referring back to FIG. 2, the set of basisformation elements 220 a-s include elements that can be represented asbasis formation element 220 i shown in FIG. 7. Generally, each suchbasis formation element includes a representative transformation element410 i and a (e.g., LTI) filter element 420 i. The transformationelements are generally non-linear (e.g., polynomial) and memoryless,represented as v_(i)[n]=ƒ_(i)(u[n]). Various functional forms may beused, for example, ƒ(u)=|u|², ƒ(u)=|u|³, ƒ(u)=u|u|², etc. The filterelements are generally linear and time invariant (LTI), for example,implementing one-pole or two-pole linear infinite-impulse-response (IIR)filters. For example, the poles of such filters may correspond to timeconstants of 1 to 4 samples and Q factors of 10. In general, at leastsome of the basis transformations include transformations (i.e., v_(i)[n]=u[n]) and/or pure delay filters (i.e., w_(i) [n]=v_(i)[n−τ]) for oneor more values of τ.

Continuing to refer to FIG. 7, in some examples, the non-linearcombination of the basis functions uses a balanced polynomialcomputation element 230, which can be represented in a general form as:

${y\lbrack n\rbrack} = {{H\left( {{w_{1}\lbrack n\rbrack},\ldots\mspace{14mu},{w_{S}\lbrack n\rbrack}} \right)} = {\sum\limits_{k}{a_{k}\left( {\left( {\prod\limits_{i}\left( {w_{i}\lbrack n\rbrack} \right)^{b_{k,i}}} \right)\left( {\prod\limits_{j}\left( {w_{i}^{*}\lbrack n\rbrack} \right)^{c_{k,j}}} \right)} \right)}}}$where for w=a+jb, where j=√{square root over (−1)}, and w*=a−jbrepresents the complex conjugate of w, and therefore w w*=|w|², andwhere for each term (k) the degree (Σ_(j)b_(k,i)) of the non-conjugatedterms is one greater than the degree (Σ_(j)c_(k,j)) of the conjugatedterms, that is

${\sum\limits_{i}b_{k,i}} = {1 + {\sum\limits_{j}c_{k,j}}}$Examples of such functions include H(w₁, w₂)=|w₁|² w₂−3w₁ ²w₂*(i.e.,a₁=1, a₂=−3, b_(1,1)=1, b_(1,2)=1, c_(1,1)=1, c_(1,2)=0, b_(2,1)=2,b_(2,2)=0, c_(2,1)=0, c_(2,2)=1) and H(w₁, w₂, w₃)=−j w₁ w₁w₂*+w₃.

Referring to FIG. 8, in some embodiments, some or all of the basisformation blocks 220 a-s may use “non-polynomial” forms. For example, asillustrated in FIG. 8, a normalization block 820 i may be used tonormalize a basis value by dividing by an average value (e.g., a longtime scale decaying average). It should be recognized that this type ofnormalization is only an example of a non-polynomial form of basisformation.

Referring back to FIG. 2, the output z[n] is then downsampled andfiltered, for example, to the original sampling rate of the input x[m]to yield the output y[m]. In some examples, this downsampling may beomitted, or the sampling rate of the output may be between the samplingrate of the input and the upsampled rate. In some examples, an optionalLTI filtering stage 242 is applied at the output of the DPD 200 prior topassing the signal to the transmit chain.

The structure of the DPD described above is robust to variation duringoperation and does not necessarily have to be adapted quickly duringoperation in order to maintain the linearization of the system. Forexample, the parameters for the DPD may be estimated once for longperiods of operation, for example, being estimated during manufacturingor deployment of the system.

Referring back to FIG. 5, in an approach to estimation of the parametersΘ for the DPD, a receive chain 330 processes a sensing of the outputp(t), and though substantially linear demodulation, and digitization,produces an digital output q[m] at the same sampling rate as the inputy[m] of the transmit chain. Note that as introduced above, thisestimation may be uses as part of formation of the coefficients of thedatabase 344, and may also be used in operational adjustment of thecoefficients as illustrated in FIGS. 4 and 6.

In some examples, data comprising input to the transmit chain, y[m], andcorresponding sensed (i.e., including demodulation) output of thetransmit chain, q[m], are collected in a series of iterations, with theparameters Θ={a_(k)} being determined from the collected data. In someexamples, the collected data sequences e_(K-1)[m]., representing thepre-distortion added to the original signal, are obtained throughiterations as follows:

-   -   Assume q₀[m]=y₀ [m]+e₀ [m], where y₀[m] is the original signal        sequence without the pre-distortion.    -   Iterate the training sequence y₁ [m]=y₀ [m]−e₀ [m], and find e₁        [m]=q₁[m]−y₀[m].    -   Continue iterating y_(k)[m]=y₀[m]−e_(k-1)[m], and find        e_(k)[m]=q_(k)[m]−y₀[m], for k=2,3, . . . .    -   After a final iteration (K), the pre-distorter is configured        such that for an input q_(k)[m]=y₀[m]+e_(k)[m] the predistorter        produces an output y_(K)[m]=y₀[m]−e_(K-1)[m]

In an alternative approach, the nonlinear transformation of y₀ [m] toyield q₀[m] is used to characterize the transmit chain (e.g., accordingto a different parameterization than is used for the pre-distorter). Theparameters Θ={a_(k)} are then determined to best “invert” the estimatedcharacteristics of the transmit chain.

In some implementations, the parameters Θ are determined based on apredictor, which accepts parameters, for instance, temperature, powersupply voltage (Vdd), sampling rate, modulation mode, frequency band,part signature (e.g., obtained by short in-fab part characterizationusing a few tones or a special transmit sequences), and part age. Basedon these, the predictor unit determines the regime of operation for thecompensator and outputs updated coefficients for the compensator andselects parameters of a predetermined set of parameters.

Implementations of the approaches described above may use hardware,software, or a combination of hardware and software. Software mayinclude instructions for a general purpose, a special purpose processoror a heterogeneous processor, with the instructions being stored on anon-transitory machine readable medium and read from the medium forexecution by the processor. The instructions may be machine level, ormay be represented in programming language form. In some examples, atleast some of the transmit chain is implemented in software, and the DPDapproach is implemented as further software executed on the samplesignal processor or system that implements that part of the transmitchain. In some examples, the software is executed on a processorspecifically dedicated to implementation of the DPD.

At least some implementations of the DPD make use of circuitry, whichgenerally includes circuitry for digital signal processing (e.g.,arithmetic computation circuitry) which may be dedicated (e.g., asapplication specific integrated circuits, ASICs, or Field-ProgrammableGate Arrays) to particular functions described above and/or may becontrolled by software instructions that implement the functions. Insome implementations, a computer accessible storage medium includes adatabase representative of some or all of a DPD 200. Generally speaking,a computer accessible storage medium may include any non-transitorystorage media accessible by a computer during use to provideinstructions and/or data to the computer. For example, a computeraccessible storage medium may include storage media such as magnetic oroptical disks and semiconductor memories. Generally, the databaserepresentative of the system may be a database or other data structurewhich can be read by a program and used, directly or indirectly, tofabricate the hardware comprising the system. For example, the databasemay be a behavioral-level description or register-transfer level (RTL)description of the hardware functionality in a high level designlanguage (HDL) such as Verilog or VHDL. The description may be read by asynthesis tool which may synthesize the description to produce a netlistcomprising a list of gates from a synthesis library. The netlistcomprises a set of gates which also represent the functionality of thehardware comprising the DPD The netlist may then be placed and routed toeither produce the configuration bitfile for the Field-Programmable GateArray or produce a data set describing geometric shapes to be applied tomasks. The masks may then be used in various semiconductor fabricationsteps to produce a semiconductor circuit or circuits corresponding tothe DPD In other examples, Alternatively, the database may itself be thenetlist (with or without the synthesis library) or the data set

It is to be understood that the foregoing description is intended toillustrate and not to limit the scope of the invention, which is definedby the scope of the appended claims. Other embodiments are within thescope of the following claims.

What is claimed is:
 1. A digital compensator for a signal chaincomprising at least one analog amplification element, the digitalcompensator comprising: an input for receiving a desired signal; anoutput for providing a compensated signal; a storage for a plurality ofcoefficients; and a signal processor coupled to the input and to theoutput for processing a desired signal to produce the compensated signalaccording to the plurality of coefficients; wherein the signal processorcomprises a basis formation stage coupled to a basis combination stage;the basis formation stage includes a plurality of basis formationelements, each configured to produce a basis signal that depends on thedesired signal provided to the input; at least some of the basisformation elements each includes a non-linear element configured toproduce a non-linear transformation of the desired signal, and a filterconfigured to produce a time filtering of the non-linear transformation;the basis combination stage is configured to accept the plurality ofbasis signals from the basis formation elements, and to produce acombined signal from said basis signal according to the plurality ofcoefficients; and the digital compensator is configured to provide thecompensated signal at the output according to the combined signalproduced by the basis combination stage.
 2. The digital compensator ofclaim 1 wherein the digital compensator is coupled to a signal chaincomprising a transmit chain of a radio frequency communication system.3. The digital compensator of claim 1 further comprising a linear timeinvariant filter coupled between the input and the basis formationstage.
 4. The digital compensator of claim 3 wherein the filter coupledbetween the input and the basis formation stage is configured accordingto characteristics of the signal chain.
 5. The digital compensator ofclaim 1 wherein at least some of the non-linear elements of the basisformation elements each implements a polynomial transformation.
 6. Thedigital compensator of claim 5 wherein a polynomial transformationimplemented by at least one of the non-linear elements accepts an inputu and produces an output of the form |u|^(k) or u|u|^(k) for a positiveinteger k.
 7. The digital compensator of claim 1 wherein at least someof the filters of the basis formation elements each implements linearinfinite-impulse-response (IIR) filter.
 8. The digital compensator ofclaim 1 wherein at least some of the basis formation elements eachcomprises a non-polynomial nonlinear element configured to process theoutput of the filter and produce an output of the basis formationelement that depends on a history of the input of the non-polynomialnonlinear element.
 9. The digital compensator of claim 8 wherein atleast some of the basis non-polynomial nonlinear elements arenormalization elements configured to process the output of the filterand produce an output of the basis formation element that depends on ahistory of the input of the normalization element.
 10. The digitalcompensator of claim 1 wherein the basis combination stage is configuredto implement a balanced polynomial combination of the basis signals. 11.The digital compensator of claim 10 wherein the basis combination stageis configured to accept basis signal values w₁ to w_(S), for a positiveinteger S, and to produce a combined signal that represents a sum overinteger indices k of products over integer indices i and j$\sum\limits_{k}{a_{k}\left( {\left( {\prod\limits_{i}\left( {w_{i}\lbrack n\rbrack} \right)^{b_{k,i}}} \right)\left( {\prod\limits_{j}\left( {w_{i}^{*}\lbrack n\rbrack} \right)^{c_{k,j}}} \right)} \right)}$where w* denotes a complex conjugate of w, the terms a_(k) depend on thecoefficients, and integer exponents b_(k,i) and c_(k,j) of the termssatisfy ${\sum\limits_{i}b_{k,i}} = {1 + {\sum\limits_{j}{c_{k,j}.}}}$12. The digital compensator of claim 1 further comprising a coefficientinterpolator configured to provide values of the coefficients.
 13. Thedigital compensator of claim 12 wherein the coefficient interpolator isconfigured to access a database to determine the values of thecoefficients according to at least one of a part signature andenvironment variables.
 14. The digital compensator of claim 13 whereinthe coefficient interpolator is further configured to access the partsignature from a storage coupled to or associated with the signal chain,the pan signature representing substantially unique characteristics ofsaid signal chain.
 15. The digital compensator of claim 14 wherein thepart signature substantially includes at least one quantity representinga non-linear characteristic of the signal chain.
 16. The digitalcompensator of claim 13 wherein the coefficient interpolator is furtherconfigured to access the environment variables from a storageoperationally coupled to the signal chain, the environment variables inoperation representing operational and/or environmental characteristicsof the operating signal chain.
 17. The digital compensator of claim 16wherein the environment variables include a quantity representing atleast one of an operating temperature and a supply voltage.
 18. A methodfor digital compensation of a signal chain comprising at least oneanalog amplification element, the method comprising: receiving a desiredsignal; processing the desired signal to produce the compensated signalaccording to a plurality of coefficients; and providing the compensatedsignal to the signal chain; wherein processing the desired signalcomprises processing a signal that depends on the desired signal in abasis combination stage, including producing a plurality of basissignals, each depending on the desired signal, wherein producing eachbasis signal of at least some of the basis signals includes performing anon-linear transformation of the desired signal and time filtering thenon-linear transformation of the desired signal, combining the pluralityof basis signals according to the plurality of coefficients to produce acombined signal, and determining the compensated signal according to thecombined signal.
 19. The method for digital compensation of claim 18wherein providing the compensated signal to the signal chain comprisesproviding said compensated signal to a transmit chain of a radiofrequency communication system.
 20. The method for digital compensationof claim 18 further comprising applying a linear time invariant filterto the desired input signal prior to processing in the basis formationstage.
 21. The method for digital compensation of claim 20 furthercomprising configuring the linear time invariant filter according tocharacteristics of the signal chain.
 22. The method for digitalcompensation of claim 18 wherein performing a non-linear transformationof the desired signal comprises applying a polynomial transformation.23. The method for digital compensation of claim 22 wherein thepolynomial transformation includes accepts an input u and producing anoutput of the form |u|^(k) or u|u|^(k) for a positive integer k.
 24. Themethod for digital compensation of claim 18 wherein time-filtering inthe basis combination stage includes a linear infinite-impulse-response(IIR) filtering.
 25. The method for digital compensation of claim 18wherein performing a non-linear transformation of the desired signalcomprises applying a non-polynomial nonlinear transformation andprocessing an output of the filter to depend on as history of an inputof the non-polynomial nonlinear transformation.
 26. The method fordigital compensation of claim 25 wherein at least some of thenon-polynomial nonlinear transformations include normalizationconfigured to process the output of the filter and produce an outputthat depends on a history of the input of the normalization.
 27. Themethod for digital compensation of claim 18 wherein the basiscombination stage implements a balanced polynomial combination of thebasis signals.
 28. The method for digital compensation of claim 27wherein the basis combination stage accepts basis signal values w₁ tow_(S), for a positive integer S, and produces a combined signal thatrepresents a sum over integer indices k of products over integer indicesi and j$\sum\limits_{k}{a_{k}\left( {\left( {\prod\limits_{i}\left( {w_{i}\lbrack n\rbrack} \right)^{b_{k,i}}} \right)\left( {\prod\limits_{j}\left( {w_{i}^{*}\lbrack n\rbrack} \right)^{c_{k,j}}} \right)} \right)}$where w′ denotes a complex conjugate of w, the terms a_(k) depend on thecoefficients, and integer exponents b_(k,i) and c_(k,j) of the termssatisfy ${\sum\limits_{i}b_{k,i}} = {1 + {\sum\limits_{j}{c_{k,j}.}}}$29. The method for digital compensation of claim 18 further comprisingapplying a coefficient interpolator to provide values of thecoefficients.
 30. The method for digital compensation of claim 29wherein the coefficient interpolator accesses a database to determinethe values of the coefficients according to at least one of a partsignature and environment variables.
 31. The method for digitalcompensation of claim 30 wherein the coefficient interpolator accessesthe part signature from a storage coupled to or associated with thesignal chain, the part signature representing substantially uniquecharacteristics of said signal chain.
 32. The method for digitalcompensation of claim 31 wherein the part signature substantiallyincludes at least one quantity representing a non-linear characteristicof the signal chain.
 33. The method for digital compensation of claim 30wherein the coefficient interpolator accesses the environment variablesfrom a storage operationally coupled to the signal chain, theenvironment variables in operation representing operational mid/orenvironmental characteristics of the operating signal chain.
 34. Themethod for digital compensation of claim 33 wherein the environmentvariables include a quantity representing at least one of an operatingtemperature and a supply voltage.
 35. A non-transitory machine-readablemedium having instructions stored thereon, execution of the instructionscausing a data processing system to: receive a desired signal; processthe desired signal to produce the compensated signal according to aplurality of coefficients; and provide the compensated signal to thesignal chain; wherein processing the desired signal comprises processinga signal that depends on the desired signal in a basis combinationstage, including producing a plurality of basis signals, each dependingon the desired signal, wherein producing each basis signal of at leastsome of the basis signals includes performing a non-lineartransformation of the desired signal and time filtering the non-lineartransformation of the desired signal, combining the plurality of basissignals according to the plurality of coefficients to produce a combinedsignal, and determining the compensated signal according to the combinedsignal.
 36. A non-transitory machine-readable medium having a designstructure encoded thereon, said design structure comprising elements,said design structure imparting functionality to a computer-aided designsystem when processed by said system to generate a machine-executablerepresentation of a digital compensator, wherein said digitalcompensator comprises: an input for receiving a desired signal; anoutput for providing a compensated signal; a storage for a plurality ofcoefficients; and a signal processor coupled to the input and to theoutput for processing a desired signal to produce the compensated signalaccording to the plurality of coefficients; wherein the signal processorcomprises a basis formation stage coupled to a basis combination stage;the basis formation stage includes a plurality of basis formationelements, each configured to produce a basis signal that depends on thedesired signal provided to the input; at least some of the basisformation elements each includes a non-linear element configured toproduce a non-linear transformation of the desired signal, and a filterconfigured to produce a time filtering of the non-linear transformation;the basis combination stage is configured to accept the plurality ofbasis signals from the basis formation elements, and to produce acombined signal from said basis signal according to the plurality ofcoefficients; and the digital compensator is configured to provide thecompensated signal at the output according to the combined signalproduced by the basis combination stage.